Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              menſurabilis lateri ſui quadrati, falſum erit dicere diametrum eſſe com­
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              menſurabilem prædicto lateri, quod autem falſum eſt, illud non eſt; igitur
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              impoſsibile eſt ſcire diametrum eſſe commenſurabile.</s>
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              21</s>
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              <s id="s.000882">Hoc eodem cap. plura dicuntur de Principijs Demonſtrationis, ſiue ſcien­
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              tiæ, vt ſunt Dignitates, Poſitiones, Definitiones, & ſimilia, quæ quo modo
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              ſe habeant, & quo modo illis Demonſtrationes innitantur, optimè ex con­
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              templatione primi libri Elem. Euclidis percipi poteſt. </s>
              <s id="s.000883">vt propterea benè ij
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              ſentiant, inter quos præcipui ſunt Toletus, & Zabarella, qui aſſerunt, Ariſt.
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              Mathematicas ſcientias tamquam typum perfectiſsimarum ſcientiarum
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              ſibi ob oculos propoſuiſſe; ex quo typo veræ ſcientiæ deſcriptionem his li­
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              bris complectaretur.</s>
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              22</s>
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              <s id="s.000886">Eodem tex. 5.
                <emph type="italics"/>
              (Ponit enim Arithmeticus vnitatem indiuiſibilem eſſe ſecun­
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              dum quantum)
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              hoc quamquam non ponatur ab Arithmeticis expreſsè, præ­
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              ſupponitur tamen ab eis: nuſquam enim Euclides in totis tribus Arithme­
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              ticis libris, infra vnitatem deſcendit, vt propterea appareat, ipſam in quan­
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              titate diſcreta eſſe minimum, & indiuiſibile. </s>
              <s id="s.000887">Verum dubitabit fortè quiſ­
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              piam hoc modo, ſi vnitas minimum,
                <expan abbr="atq;">atque</expan>
              indiuiſibile eſt in quanto diſcreto,
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              qua igitur ratione Arithmetici practici eam diuidunt in dimidium, in trien­
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              tem, in quadrantem, & alijs ſimiliter modis, vnde numeri illi, qui fractio­
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              nes appellantur, exurgunt? </s>
              <s id="s.000888">Reſpondemus,
                <expan abbr="quotieſeunq;">quotieſcunque</expan>
              vnitas diuiditur ab
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              Arithmeticis, tunc ipſi eam accipiunt tanquam totum quoddam
                <expan abbr="cõtinuum">continuum</expan>
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              in plures partes diuiſibile: ſiue tanquam aggregatum quoddam vnitatum,
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              quæ vnitates ſunt partes illius, vt quando dicunt, vnum horæ quadrantem,
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              vel duos horæ quadrantes, vel tres horæ quadrantes, accipiunt horam tan­
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              quam aggregatum quatuor quadrantum, & propterea numeri illi 1/4. 2/4. 3/4.
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              & ſimiles fractiones, nihil aliud ſunt, quam numeri partium vnius horæ: ex
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              quo patet huiuſmodi fractiones omnes reduci ad numeros integros, qui
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              enim dicit tres quadrantes 3/4. dicit tres partes alicuius totius, quod intel­
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              ligitur diuiſum eſſe in 4. æquales partes, ex quibus illæ tres tantummodo
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              numerat.</s>
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              <s id="s.000891">Tex. 9.
                <emph type="italics"/>
              (Per ſe autem,
                <expan abbr="quæcunq;">quæcunque</expan>
              & inſunt in eo, quod quid eſt, vt triangulo li­
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              nea, & lineæ punctum; ſubſtantia
                <expan abbr="namq;">namque</expan>
              ipſorum ex his eſt, & in oratione dicen­
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              te, quid eſt, inſunt)
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              aggreditur explicare quænam ſint ea, quæ per ſe dicun­
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              tur:
                <expan abbr="quotq́">quotque</expan>
              ; modis dicatur aliquid per ſe. </s>
              <s id="s.000892">quorum primus eſt, ea ſcilicet,
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              per ſe de aliquo ſubiecto dici,
                <expan abbr="quæcunq;">quæcunque</expan>
              in definitione illius ponuntur, cu­
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              iuſmodi ſunt linea, & punctum, quæ per ſe prædicantur, illa de triangulo,
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              iſtud de linea; in definitione enim trianguli ponitur linea recta, quia linea
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              recta dum terminat illam ſuperficiem, quæ dicitur triangulus illi trianguli
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              naturam impertitur, & ideo triangulus definitur ſic, triangulus eſt figura
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              tribus lineis rectis terminata. </s>
              <s id="s.000893">ſimiliter in definitione lineæ, non infinitæ,
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              ſed finitæ, & terminatæ ponitur punctum, quia duo puncta, quæ ſunt extre­
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              ma illius, faciunt, vt ea ſit line a finita, & definitur ſic, linea finita eſt lon­
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              gitudo, cuius extrema ſunt puncta. </s>
              <s id="s.000894">quamuis autem hæc definitio apud Eu­
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              clidem expreſſa non habeatur, tamen ex definitionibus ipſius præſertim ſe­
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              cunda, tertia, & quarta elici poteſt.</s>
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              24</s>
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            <p type="main">
              <s id="s.000897">Eodem tex. 9.
                <emph type="italics"/>
              (Et
                <expan abbr="quibuſcunq;">quibuſcunque</expan>
              inexiſtentium ipſis, ipſæ ſunt in oratione, quid
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
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    </archimedes>
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